Test Preparation on CAT paper 3

In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?

A function f(n) is defined as f(n) = (n - 1) (n) (n + 1). What is the remainder when f(n) is divided by 11 given that n = 1247?

If a and b are positive integers such that 4a + 5b - 100 = 0, then find the total number of solutions.

A number X, when expressed in base ‘n’, is of form AB, where A and B are two non Zero digits. If the number X is such that (AB)n = 4 (BA), then what is the decimal equivalent of (AB) when n takes the minimum possible value?

PQRS is a square, while diagonals PR and QS coincide with the x and y-axis respectively. Side PQ lies on the line x + y + 3 = 0. Side RS lies on which of the following lines?

The local park at Raghu’s house is in the shape of a triangle. There are 4 posts along the longest side of the park and 2 and 3 posts along the other two sides respectively. If none of these posts is at any of the comers of the park, find the number of triangles that are possible with vertices at these posts.

If the two curves in the figure given alongside have the magnitudes of their respective minimum and maximum values as equal, which of the following pair of equations may represent the two curves?

All Analysts are Engineers. One-third of all Engineers are Analysts. Half of all Technicians are Engineers. Only one Technician is an Analyst. Eight Technicians are Engineers. If the number of Engineers is 90, how many Engineers are neither Analysts nor Technicians